1. Field of the Invention
This invention relates generally to the manufacture of three dimensional planar electric circuits, and more particularly to a method and apparatus for determining the characteristics of the circuits at high frequencies by the use of sub-sectional electromagnetic analysis.
The characteristics of three dimensional planar electronic circuits at high frequencies are important both for fabricating microwave circuits, such as micro strip wave guides and the like that are used in the generation, transmission and reception of microwave signals. High frequency electromagnetic characteristics are also increasingly important in digital circuits that operate at ever higher frequencies. Digital circuits operating in a range of 500 mH are common today, and even higher operating frequencies are expected to be common in the future.
2. Description of the Related Art Including Information Disclosed Under 37 C.F.R. .sctn..sctn. 1.97, and 1.98
One method for analyzing arbitrary planar circuits is described by Rautio and Harrington in "An Electromagnetic Time-Harmonic Analysis of Shielded Micro Strip Circuits", IEEE Transactions of Microwave Theory and Techniques, Vol., MTT-35, No. 8, August 1987. The circuit metallization is divided into small rectangular sub-sections. We will refer to this dividing as meshing. An explicit surface current distribution is assumed to exist in each subsection. The tangential electric field created by the current in each subsection are determined and the magnitude of the current in all subsections is adjusted, so that the weighted residual of the total tangential electric field goes to zero. The surface currents are then determined, and the electromagnetic characteristics of the circuit are known therefrom.
While meshing a circuit into arbitrarily small rectangles can produce any desired degree of accuracy, the step of adjusting the magnitude of the current in each subsection involves inversion of a matrix whose size increases as the square of the number of subsections. Analysis time becomes expensive, and eventually, the time taken to make the analysis is so long that the desired degree of accuracy cannot be obtained.
There is a need for a method and apparatus for determining the electromagnetic characteristics of 3D planar circuits that permits a greater degree of accuracy to be obtained in a reasonable time than has heretofore been possible. In order to reduce the time needed to characterize the circuit, fewer subsections must be used to represent the circuit. The time required to invert a non-sparse matrix increases with the cube of the number of subsections. In addition, if the dimensions of the subsection are halved, the area of the subsection is one-fourth the size of the original subsection and four times the number of subsections are required to cover the same area. The resulting matrix inversion takes 64 times longer.
This invention greatly increases the accuracy with which the amplitude of the current on a subsection can be determined, by utilizing a new meshing technique that we call conformal meshing. Conformal meshing selects basis functions such that an accurate representation of the actual current distribution in a circuit can be realized with a much smaller number of subsections than has been heretofore possible. Conformal meshing permits a circuit to be analyzed with an error that heretofore would correspond only to meshing with a very small subsize, while maintaining the speed normally seen when using a large cell size.
One method for reducing the number of rectangular subsections is to combine rectangular subsections with triangular subsections. Triangles are used to smooth out stair case edges produced with rectangular subsections. Also, merged rectangles have been used in regions where current changes slowly. More specifically, currents are normally high at the edges of planar circuits at high frequencies, and much lower in the centers of such circuits. By using narrow subsections at the edges to represent the high edge currents and wider subsections in the interior of the circuit where the current is more uniform, the number of subsections can be reduced. A problem arises with this method, however, in that these approaches permit only uniform current distribution across the width of the cell. The current distribution along the length of the cell can vary in a piece-wise linear manner, but if the subsection has the same width as a transmission line, for example, the subsection forces uniform current across the width of the transmission line. In reality, the current is very high at the edges of the line due to the edge effect, and lower and more uniform at the center. This discrepancy between the actual current distribution and the current distribution forced by the use of a single subsection results in about 6% error, which is more than can be tolerated in many applications.
Rectangular and triangular meshing have characterized the piece-wise linear change in current variation along the length of the cell by using "roof-top" functions described by Glisson and Wilton in "Simple and Efficient Numerical Methods for Problems of Electromagnetic Radiation and Scattering from Surfaces", IEEE Transactions on Antennas and Propagation Vol. AP-28, No. 5, September 1980.
The present invention generalizes the roof top function, so that it can be used for subsections of arbitrary shape.
It is an object of the invention to greatly reduce the number of subsections required to completely mesh a 3D planar circuit. Conformal meshing in accordance with the invention provides subsections that are bent to fit the edge of the 3D planar circuit. The present invention utilizes subsections in which the current distribution is not uniform from edge to edge, but is modified to accurately represent the high edge currents caused by the edge effect that occurs in circuits operated at high frequencies.
Subsections in accordance with this invention are not limited to simple rectangles and triangles. Subsections used in meshing a curving transmission line can be curved to fit the curving edge of the transmission line, so that the multiplicity of rectangular or triangular subsections heretofore required is no longer needed. By providing subsections that take the high edge current into account, the analysis error obtained through the use of the present invention is much lower than could heretofore be obtained with a similar number of subsections. Because the subsections conform to the edge of the planar 3D circuit, very few subsections are required, and this invention produces the magnitude of error heretofore obtainable only with a large number of small subsections combined with the speed heretofore obtained only with very large subsections (which produce large errors).